Abstract
We study the relationship between postulation and reduction vectors of admissible multigraded filtrations $\mathcal{F}= \{\mathcal{F} (\underline{n})\}_{\underline{n} \in \mathbb{Z} ^s}$ of ideals in Cohen-Macaulay local rings of dimension at most two. This is enabled by a suitable generalization of the Kirby-Mehran complex. An analysis of its homology leads to an analogue of Huneke's fundamental lemma which plays a crucial role in our investigations. We also clarify the relationship between the Cohen-Macaulay property of the multigraded Rees algebra of $\mathcal{F} $ and reduction vectors with respect to complete reductions of $\mathcal{F} $.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.